Basis set limitations on the ab initio calculation of stopping cross-sections via generalized oscillator strengths

Ab initio treatment of the first Born electronic stopping cross-section for a bare proton incident upon atomic Be is attempted via a large-basis (15s13p6d3f contracted to 9s13p6d3f) polarization propagator calculation of the generalized oscillator strength distribution (GOSD). The calculated GOSD fails to satisfy the Bethe sum rule for moderately high values of collisional momentum transfer in spite of asymptotic augmentation of the calculated GOSD by a hydrogen-like contribution. A simple model shows that the BSR violation introduces unsystematic spurious contributions to the stopping cross-section. The failure illustrates a shortcoming in the conventional approach to optimizing finite basis sets and shows that predictive calculation of electronic stopping in real systems requires continued development and use of judiciously selected approximate methods.